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\begin{equation}
\begin{aligned}
&amp;y^{\prime \prime}+b y^{\prime}+c y=\frac{1}{2} e^{(\alpha+ i \beta) x} P_n(x) +\frac{1}{2} e^{(\alpha- i \beta) x} P_n(x) \quad (\textrm{can be decomposed into two parts})\\
&amp; \to y^{\prime \prime}+b y^{\prime}+c y=\frac{1}{2} e^{(\alpha+ i \beta) x} P_n(x)\\
&amp;\quad y^{\prime \prime}+b y^{\prime}+c y=\frac{1}{2} e^{(\alpha- i \beta) x} P_n(x) 
\end{aligned}\tag{3.6.13}
\end{equation}
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